An image processing system for printing and the like generally includes a host computer for forming and outputting print data to be printed, and a printing apparatus which prints an image (color image) of a plurality of colors on a printing medium such as a printing sheet of paper in accordance with input print data from the host computer. In this image processing system, the host computer processes image data by three primary colors R (red), G (green), and B (blue), because the computer performs interactive processing with an operator by using a display. On the other hand, the printing apparatus prints data on a printing medium by ink colors C (cyan), M (magenta), Y (yellow), and K (black), so the apparatus usually processes image data by these four colors CMYK.
An inkjet printing apparatus as one printing apparatus sometimes uses cyan (light cyan, to be referred to as LC hereinafter) and magenta (light magenta, to be referred to as LM hereinafter) having lower density than common inks, in addition to the four types of inks described above. This is so because an inkjet printing apparatus prints data by spraying slight amounts of inks onto the surface of paper, and so dots of the sprayed inks are visible in a high-lightness portion close to white. Examples of a method of improving this drawback are to decrease dot diameters on a printing surface by reducing amounts of sprayed inks, and to make dots difficult to recognize by decreasing the dye concentrations of inks. As the latter method, LC and LM inks having low density are presently often used together with C and M inks which tend to produce considerable granularity. This greatly improves the granularity.
To this end, RGB values depending on a display must be transformed into printing colors such as CMYK unique to a printing apparatus. Various methods have been proposed as a method of this color transform. One is a method called direct mapping. In this method, CMYK values described in a lookup table (to be referred to as a “color transform LUT” or simply as a “LUT” hereinafter) prepared beforehand are directly referred to in accordance with input RGB values. The use of this method makes nonlinear transform or complicated transform possible, and this makes finer image design feasible.
Since color transform is generally three- or four-dimensional transform, an enormous memory capacity is necessary if output values corresponding to all input values are described in a color transform LUT. Also, the formation of such a color transform LUT is time-consuming and impractical. For example, when each value of input RGB has 8 bits and each value of output CMYK has 8 bits, the size of a color transform LUT describing the correspondence of all combinations is approximately 2 gigabytes. Additionally, CMYK values corresponding to about 16,700,000 input RGB values must be found, so the formation of this color transform LUT requires much labor.
To save the memory capacity and simplify the formation of a color transform LUT, therefore, the general approach is to use a color transform LUT interpolation method. In this method, an input color space is divided into appropriate unit solids. Input/output relationships are stored as a color transform LUT only on coarse lattice points, and values between these coarse lattice points are calculated by an interpolating operation. For example, a color space is divided into tetrahedrons, pyramids, or cubes, and each axis is generally divided into 8 to 32 portions.
FIG. 1 shows an example of a color transform LUT. In this LUT, each of RGB axes is divided into 16 portions. The LUT begins with black (R, G, B)=(0, 0, 0), loops 16 times in the order of B, G, and R, and ends with white (R, G, B)=(255, 255, 255). Corresponding values (signal values) represent cyan (C), magenta (M), yellow (Y), and black (K) in this order from the left. The following description is based on this color transform LUT in which each of RGB axes are thus divided into 16 portions.
FIG. 2 is a graph showing an example of the correspondence between input RGB signal values and output CMYK signal values of only a gray line, from white (R, G, B)=(255, 255, 255) to black (R, G, B)=(0,0,0), extracted from a color transform LUT of an inkjet printing apparatus which prints data by using four types of inks (C, M, Y, and K). This graph shows that data is printed by three types of inks, cyan (C), magenta (M), and yellow (Y), from white (R, G, B)=(255, 255, 255) to a lattice point (R, G, B)=(96, 96, 96), that these inks are gradually replaced with black ink from (R, G, B)=(96, 96, 96), and that only black ink (K) is used at (R, G, B)=(0, 0, 0).
FIG. 3 is a graph showing an example of the correspondence between input RGB signal values and output CMYK signal values of only a gray line extracted from a color transform LUT of an inkjet printing apparatus which prints data by using six types of inks (C, Y, K, LC, and LM). This graph shows that data is printed by three types of inks, Y, LC, and LM, from white R=G=B=255 to a lattice point R=G=B=208. From R=G=B=208, inks C, M, and Y are introduced and inks Y, LC, and LM are reduced. From R=G=B=64, K ink is introduced and C, M, and Y inks are reduced. Finally, only the ink K is used at R=G=B=0.
The purposes of these processes are to reduce the granularity of a printed image. An inkjet printer prints data by spraying slight amounts of inks onto the surface of a printing sheet. Therefore, dots of the sprayed inks are discernible in a high-lightness portion close to white, and this worsens the granularity. Examples of a method of improving this drawback are to decrease dot diameters on a printing surface by reducing amounts of sprayed inks, and to make dots difficult to recognize by decreasing the dye concentrations of inks. In the gray line shown in FIG. 2, ink amounts are increased by using C, M, and Y inks without using K ink in a high-lightness portion, thereby reducing low-frequency components of the spatial frequency and improving the granularity. In the gray line shown in FIG. 3, the granularity is improved by using LC and LM inks without using C, M, and K inks in a high-lightness portion. Since the ink amounts used increase, however, inks blot on the surface of a printing sheet, and the ink consumption amount increases. These drawbacks have a tradeoff relationship with the granularity.
FIG. 4 is a graph showing an example of the correspondence between input RBG signal values and output CMYK signal values on a line from red (R, G, B)=(255, 0, 0) to black (R, G, B)=(0, 0, 0) in a color transform LUT. As shown in FIG. 4, data is generally printed by initially using cyan ink (C) as a complementary color to red and then using black ink (K). With this method, the granularity can be reduced similar to the gray line from white to black.
Although there are problems of ink blot and an increase in the ink consumption amount as described above, a difference from the gray line from white to black is that the size of color space also changes. As shown in FIG. 5 which is a view of projection onto an a*-b* plane, the color reproduction region of colors generated on a printing sheet by subtractive mixture largely differs from that of colors generated on a monitor (display) by additive mixture. An apparatus such as an inkjet printer which prints hard copies is largely inferior to a monitor in color generation. Hence, data is preferably printed by increasing the color reproduction region as large as possible, since the image becomes close to a monitor image.
FIG. 6 is a graph showing an example of the correspondence between input RGB signal values and output CMYK signal values on a line from red to black in a color transform LUT, when only black ink (K) is used without using any complementary color ink.
FIG. 7 shows a color reproduction region when only black ink (K) is used without using any complementary color ink as shown in FIG. 6, and a color reproduction region when complementary color ink and black ink (K) are used together as shown in FIG. 4. As FIG. 7 illustrates, the color reproduction region is larger when only black ink (K) is used. This is so because black ink can reduce lightness (L*) with a smaller ink amount. When cyan (C) is used jointly, the whole ink printing amount increases, and this reduces the saturation component. That is, the use of black ink (K) on a line from color to black results in a tradeoff relationship: the color reproduction region can be increased although the granularity increases.
Also, since cyan, magenta, yellow, red, green, and blue (to be referred to as “primary colors” hereinafter) are different in lightness and saturation, they are also different in granularity when black ink (K) is used. For example, of these six primary colors, blue having the lowest lightness produces no granularity even when no complementary color is used. In contrast, when yellow having the highest lightness is used, no black ink is preferably used because this eliminates the granularity. Accordingly, better images can be obtained by changing the start point of use of black ink in accordance with each color.
A color transform LUT is formed by taking account of the relationship between the granularity, color reproduction region, and ink consumption amount explained above. A method of forming this color transform LUT will be described below.
A color space of white, black, and a primary color is expressed by a triangle, as shown in FIG. 8, having white, the primary color, and black as apexes A, B, and C, respectively. First, sides AC and BC of the primary color are formed. As signal values from white (R, G, B)=(255, 255, 255) to the primary color, a desired density and lightness can be recorded by recording and measuring a patch. Since this determines a side AB in FIG. 8, all output signal values on the individual sides of this triangle are obtained. A color transform LUT is formed by dividing this color space into small color spaces and storing output signal values corresponding to individual lattice points. Points except for these lattice points are obtained by an interpolating operation.
A method of interpolating signal values at individual lattice points inside the above triangle when four types of inks (C, M, Y, and K) are used will be described below. Signal values at individual lattice points inside the triangle must be so interpolated as not to form any abrupt inflection point or discontinuation. If such an inflection point or discontinuation is contained, a pseudo contour is generated when an image is printed, or discontinuation or inversion of gradation occurs. Therefore, signal values inside the triangle are interpolated by using output signal values on the sides formed as described above.
As shown in FIG. 9, signal values of complementary color components can be smoothly expressed by performing linear interpolation in a direction D along a side AB connecting white and a primary color. For example, referring to FIG. 9, letting GRAYc(X0, Y) and GRAYk(X0, Y) be signal values of complementary color ink and black ink, respectively, in a position (X0, Y) on a side AC (gray line) connecting white and black, and COLORc(X1, Y) and COLORk(X1, Y) be signal values of complementary color ink and black ink, respectively, in a position (X1, Y) on a side BC connecting the primary color and black, complementary color ink Tc(X, Y) and black ink Tk(X, Y) in a position (X, Y) are calculated by the following interpolation equations.Tc(X,Y)=X×{COLORc(X1,Y)−GRAYc(X0,Y)}/(X1−X0)+GRAYc(X0,Y)Tk(X,Y)=X×{COLORk(X1,Y)−GRAYk(X0,Y)}/(X1−X0)+GRAYk(X0,Y)
By performing this interpolation for all the six primary colors, complementary color components for each of six triangles (in this specification, these triangles will be referred to as “basic triangles”) each having white, black, and a primary color as its apexes can be formed.
A method of interpolating signal values at individual lattice points inside the above triangle when six types of inks (C, M, Y, K, LC, and LM) are used will be described below. To obtain signal values inside the triangle, ink types are classified into the following two types:
(1) Inks of color components
(2) Inks of complementary color components
For example, in a white-cyan-black triangle, (1) means C and LC inks, and (2) means M, Y, K, and LM inks.
Signal values of (1) are calculated by linear interpolation in a direction E in FIG. 8. As shown in FIG. 10, horizontal and vertical directions are taken as X and Y axes, respectively. Letting GRAY(X0, Y) denote an ink signal value on a gray line and WC(X1, Y0) an ink signal value on a line from white to a primary color, an ink signal value T(X,Y) at a point (X,Y) inside the triangle is calculated byT(X,Y)=X×{WC(X1,Y0)−GRAY(X0,Y)}/(X1−X0)+GRAY(X0,Y)
Signal values of (2) are calculated by linear interpolation in the direction E in FIG. 8. Letting, similarly, CK(X1,Y) denote an ink signal value on a line from color to black, the ink signal value T(X,Y) is calculated byT(X,Y)=X×{CK(X1,Y)−GRAY(X0,Y)}/(X1−X0)+GRAY(X0,Y)
By performing the above interpolating operation in the triangle for all the six primary colors, ink signal values of the triangles having white, black, and the primary colors as apexes can be formed.
Furthermore, by combining the six basic triangles thus formed, a rectangular parallelepiped representing a color space having white, black, and the six primary colors as its apexes as shown in FIG. 11A can be formed.
Interpolation of signal values at lattice points positioned between the individual basic triangles will be explained below. As in the above case, linear interpolation is preferred in order not to form any abrupt inflection point or discontinuation. Consider, as an example, signal values on a triangular plane Y positioned between primary colors COLOR1 and COLOR2 shown in FIG. 11A and having apexes A, B, and C. FIG. 11B shows this triangular plane Y along with lattice points. Letting COLOR1c(i,j1) and COLOR1k(i,j1) be signal values of complementary color ink of COLOR1 and black ink, respectively, in a position (i,j1) in the triangular plane Y, and COLOR2c(i,j2) and COLOR2k(i,j2) be signal values of complementary color ink of COLOR2 and black ink, respectively, in a position (i,j2), complementary color ink Tc(i,j) and black ink Tk(i,j) in a position (i,j) can be calculated by interpolation as perTc(i,j)=j×{COLOR2c(i,j2)−COLOR1c(i,j1)}/(j2−j1)+COLOR1c(i,j1)Tk(i,j)=j×{COLOR2k(i,j2)−COLOR1k(i,j1)}/(j2−j1)+COLOR1k(i,j1)
By performing this interpolating operation between red and yellow, yellow and green, green and cyan, cyan and blue, blue and magenta, and magenta and red, signal values of complementary colors at lattice points positioned between the basic triangles can be determined.
As described above, to form a color transform LUT, the input/output correspondence is formed for each of a gray line from white to black, line from a primary color to black, and line from white to the primary color. This correspondence is so formed as to minimize the granularity and maximize the color reproduction region. A color transform LUT can be formed by calculating signal values at lattice points by linear interpolation on the basis of these correspondences.
When a color transform LUT is formed by the above-mentioned method, black ink signal values in a white-blue-black basic triangle are, for example, as shown in FIG. 12. When data is printed by looking up this color transform LUT, a smooth printing result is obtained. However, the granularity is conspicuous in a region A in FIG. 12. This is so because, although in a gray line no graininess is produced by introducing no black ink up to a predetermined level (FIG. 2), small black ink signal values are introduced at lattice points in the region A, and so black ink is used in a portion slightly deviated from the gray line. This phenomenon occurs not only when blue is used but also when lattice points on a gray line at which black ink is introduced differ from lattice points on a primary color-black line at which black ink is introduced.
This also applies to lattice points between the basic triangles. FIG. 13 shows examples of black ink signal values in a triangular plane positioned between a white-yellow-black basic triangle and a white-red-black basic triangle. The triangle shown in FIG. 13 has an apex E on the yellow-black axis, an apex F on the white-black axis, and an apex G on the red-black axis. If a lattice position where black ink is introduced on a side EF is different from a lattice position where black ink is introduced on a side FG, the granularity deteriorates in a region B. This is so because, as described above, small black ink signal values are introduced into lattice points in the region B as a result of linear interpolation.
Also, many recent inkjet printers use LC ink and LM ink (to be referred to as light cyan ink and light magenta ink), in addition to regular cyan ink and magenta ink (to be referred to as dark cyan ink and dark magenta ink for discrimination). When these inks having low dye concentration is used, the printed dots themselves become difficult to visually recognize. In addition, a larger number of dots must be sprayed than when regular inks are used in order to print data of the same density. This can increase high-frequency components of the spatial frequency. The result is the advantage that the granularity of an inkjet printer is greatly improved.
Even when such an inkjet printer is used, however, problems similar to those described above arise. FIG. 14 shows dark cyan ink signal values in a white-red-black basic triangle formed by the linear interpolation described earlier. As in the case of black ink, the granularity worsens by dots of dark cyan ink in a region C. This is because small dark cyan ink signal values are introduced into lattice points in the region C.
C ink can also be linearly interpolated in the direction D in FIG. 8, not in the direction E in FIG. 8, analogous to complementary color ink. When this is performed, the results as shown in FIG. 15 are obtained. In this case, a smooth LUT can be formed, but C ink is slightly introduced into a portion F in FIG. 15. As is apparent from a gray line and a white-cyan line near the portion F, this portion F is a region which can be expressed by LC ink without using C ink. When C ink is slightly introduced into this region, dots of C ink become conspicuous although low-density LC ink is used. This results in printing inferior in granularity.
As described above, in the formation of a color transform LUT, if triangles are formed and linear interpolation is performed on the basis of values on the sides of these triangles, the granularity deteriorates by complementary color ink and black ink.
This will be further explained by using a white-cyan-black triangle. FIG. 16A shows ink signal values of color component C obtained by interpolating the interior of the triangle on the basis of previously formed sides by the aforementioned prior art. FIG. 16B shows ink signal values of color component LC obtained by interpolating the interior of the triangle on the basis of previously formed sides by the aforementioned prior art.
The signal values of LC ink shown in FIG. 16B are smooth. However, the signal values of C ink shown in FIG. 16A have an inflection point as seen in the direction of an arrow A, and largely jump as seen in a portion B. If an image is printed by using this LUT, a pseudo contour is generated, or discontinuation or inversion of gradation takes place.